SRC/dormr3.f(3)

NAME
SRC/dormr3.f

SYNOPSIS

  Functions/Subroutines
subroutine dormr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info)
DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

Function/Subroutine Documentation

  subroutine dormr3 (character side, character trans, integer m, integer n, integer k, integer l, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer info)

DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

Purpose:

    !>
    !> DORMR3 overwrites the general real m by n matrix C with
    !>
    !>       Q * C  if SIDE = 'L' and TRANS = 'N', or
    !>
    !>       Q**T* C  if SIDE = 'L' and TRANS = 'C', or
    !>
    !>       C * Q  if SIDE = 'R' and TRANS = 'N', or
    !>
    !>       C * Q**T if SIDE = 'R' and TRANS = 'C',
    !>
    !> where Q is a real orthogonal matrix defined as the product of k
    !> elementary reflectors
    !>
    !>       Q = H(1) H(2) . . . H(k)
    !>
    !> as returned by DTZRZF. Q is of order m if SIDE = 'L' and of order n
    !> if SIDE = 'R'.
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply Q or Q**T from the Left
    !>          = 'R': apply Q or Q**T from the Right
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N': apply Q  (No transpose)
    !>          = 'T': apply Q**T (Transpose)
    !>

    M

    !>          M is INTEGER
    !>          The number of rows of the matrix C. M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix C. N >= 0.
    !>

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines
    !>          the matrix Q.
    !>          If SIDE = 'L', M >= K >= 0;
    !>          if SIDE = 'R', N >= K >= 0.
    !>

    L

    !>          L is INTEGER
    !>          The number of columns of the matrix A containing
    !>          the meaningful part of the Householder reflectors.
    !>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension
    !>                               (LDA,M) if SIDE = 'L',
    !>                               (LDA,N) if SIDE = 'R'
    !>          The i-th row must contain the vector which defines the
    !>          elementary reflector H(i), for i = 1,2,...,k, as returned by
    !>          DTZRZF in the last k rows of its array argument A.
    !>          A is modified by the routine but restored on exit.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A. LDA >= max(1,K).
    !>

    TAU

    !>          TAU is DOUBLE PRECISION array, dimension (K)
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i), as returned by DTZRZF.
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (LDC,N)
    !>          On entry, the m-by-n matrix C.
    !>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension
    !>                                   (N) if SIDE = 'L',
    !>                                   (M) if SIDE = 'R'
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

    !>

Definition at line 176 of file dormr3.f.

Author

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